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Question: Equation of displacement for any particle is \(s = 3t^{3} + 7t^{2} + 14t + 8m\). Its acceleration a...

Equation of displacement for any particle is

s=3t3+7t2+14t+8ms = 3t^{3} + 7t^{2} + 14t + 8m. Its acceleration at time t=1t = 1 sec is

A

10 m/s2

B

16 m/s2

C

25 m/s2

D

32 m/s2

Answer

32 m/s2

Explanation

Solution

s=3t3+7t2+14t+8 6mums = 3t^{3} + 7t^{2} + 14t + 8\mspace{6mu} m

a=d2sdt2=18t+14a = \frac{d^{2}s}{dt^{2}} = 18t + 14 at t=1 6musec⁡⇒a=32m/s2t = 1\mspace{6mu}\sec \Rightarrow a = 32m/s^{2}